Time Allowed: 3 hours Maximum Marks: 80
General Instructions:
Read the following instructions carefully and follow them:
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion-
Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study-based questions carrying 4 marks each with sub-parts of the
values of 1,1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Questions of Section B, 2 Questions of Section
C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks
questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take π = 22/7 wherever required if not stated.
11. Use of calculators is not allowed.
Section A
1. Point (0, –7) lies [1]
a) in the fourth quadrant b) on the y-axis
c) on the x –axis d) in the second quadrant
2. The sides of a triangle are 50 cm, 78 cm and 112 cm. The smallest altitude is [1]
a) 20 cm b) 40 cm
c) 30 cm d) 50 cm
3. For what value of x in the figure, points A, B, C and D are concyclic? [1]
Page 1 of 18
, a) 10 o
b) 9
o
c) 12 o
d) 11
o
4. E and F are the mid-points of sides AB and AC res. Of the △ABC ; G and H are the mid-points of the sides AE [1]
and AF res. Of the △AEF. If GH = 1.8cm, Find BC
a) 6 cm b) 7.2 Cm
c) 7.5cm d) 6.5 cm
–
5. If
5−√3
= x + y√3 , then [1]
2+√3
a) x = 13, y = 7 b) x = -13, y = - 7
c) x = -13, y = 7 d) x = 13, y = -7
6. In Figure, AB and CD are parallel lines and transversal EF intersects them at P and Q respectively. If ∠ APR = [1]
25°, ∠ RQC = 30° and ∠ CQF = 65°, then
a) x = 50°, y = 45° b) x = 60°, y = 35°
c) x = 35°,y = 60° d) x = 55°, y = 40°
7. x = 2, y = 5 is a solution of the linear equation [1]
a) x + y = 7 b) 5 x + y = 7
c) 5x +2y = 7 d) x + 2y = 7
8. When p(x) = x4 + 2x3 - 3x2 + x - 1 is divided by (x - 2), the remainder is [1]
a) 21 b) -1
c) -15 d) 0
9. The difference between two distinct irrational numbers is always [1]
a) a rational number b) both rational and irrational number
c) an irrational number d) an integer
Page 2 of 18
, 10. ABCD is a parallelogram in which ∠ ADC = 85° and side AB is produced to point E as shown in the figure. Find [1]
the value of (x + y).
a) 85° b) 95°
c) 190° d) 160°
11. The simplest form of 0.123 is¯
¯¯
[1]
a) none of these b) 41
333
c) 41
330
d) 37
330
12. The graph of the line y = -6 passes through [1]
a) (-1, 4) b) (0, 4)
c) (4, -6) d) (-6, 4)
13. Given ∠ POR = 3x and∠ QOR =2x + 10°. If ∠ POQ is a straight line, then the value of x is [1]
a) 36° b) 34°
c) 30° d) 42o
14. An irrational number between 2 and 2.5 is [1]
−
− −
− −−−
−
a) √22.5 b) √12.5
– −−
c) √5 d) √11
15. If ∠OAB = o
40 , then the measure of ∠AC B is [1]
a) 50 o
b) 80
o
c) 40 o
d) 20
o
16. The point whose abscissa is 4 and this point lies on the x-axis is: [1]
a) (0, 4) b) (4, 0)
c) (4, 4) d) (2, 4)
17. The positive solutions of the equation ax + by + c = 0 always lie in the [1]
Page 3 of 18
General Instructions:
Read the following instructions carefully and follow them:
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion-
Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study-based questions carrying 4 marks each with sub-parts of the
values of 1,1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Questions of Section B, 2 Questions of Section
C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks
questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take π = 22/7 wherever required if not stated.
11. Use of calculators is not allowed.
Section A
1. Point (0, –7) lies [1]
a) in the fourth quadrant b) on the y-axis
c) on the x –axis d) in the second quadrant
2. The sides of a triangle are 50 cm, 78 cm and 112 cm. The smallest altitude is [1]
a) 20 cm b) 40 cm
c) 30 cm d) 50 cm
3. For what value of x in the figure, points A, B, C and D are concyclic? [1]
Page 1 of 18
, a) 10 o
b) 9
o
c) 12 o
d) 11
o
4. E and F are the mid-points of sides AB and AC res. Of the △ABC ; G and H are the mid-points of the sides AE [1]
and AF res. Of the △AEF. If GH = 1.8cm, Find BC
a) 6 cm b) 7.2 Cm
c) 7.5cm d) 6.5 cm
–
5. If
5−√3
= x + y√3 , then [1]
2+√3
a) x = 13, y = 7 b) x = -13, y = - 7
c) x = -13, y = 7 d) x = 13, y = -7
6. In Figure, AB and CD are parallel lines and transversal EF intersects them at P and Q respectively. If ∠ APR = [1]
25°, ∠ RQC = 30° and ∠ CQF = 65°, then
a) x = 50°, y = 45° b) x = 60°, y = 35°
c) x = 35°,y = 60° d) x = 55°, y = 40°
7. x = 2, y = 5 is a solution of the linear equation [1]
a) x + y = 7 b) 5 x + y = 7
c) 5x +2y = 7 d) x + 2y = 7
8. When p(x) = x4 + 2x3 - 3x2 + x - 1 is divided by (x - 2), the remainder is [1]
a) 21 b) -1
c) -15 d) 0
9. The difference between two distinct irrational numbers is always [1]
a) a rational number b) both rational and irrational number
c) an irrational number d) an integer
Page 2 of 18
, 10. ABCD is a parallelogram in which ∠ ADC = 85° and side AB is produced to point E as shown in the figure. Find [1]
the value of (x + y).
a) 85° b) 95°
c) 190° d) 160°
11. The simplest form of 0.123 is¯
¯¯
[1]
a) none of these b) 41
333
c) 41
330
d) 37
330
12. The graph of the line y = -6 passes through [1]
a) (-1, 4) b) (0, 4)
c) (4, -6) d) (-6, 4)
13. Given ∠ POR = 3x and∠ QOR =2x + 10°. If ∠ POQ is a straight line, then the value of x is [1]
a) 36° b) 34°
c) 30° d) 42o
14. An irrational number between 2 and 2.5 is [1]
−
− −
− −−−
−
a) √22.5 b) √12.5
– −−
c) √5 d) √11
15. If ∠OAB = o
40 , then the measure of ∠AC B is [1]
a) 50 o
b) 80
o
c) 40 o
d) 20
o
16. The point whose abscissa is 4 and this point lies on the x-axis is: [1]
a) (0, 4) b) (4, 0)
c) (4, 4) d) (2, 4)
17. The positive solutions of the equation ax + by + c = 0 always lie in the [1]
Page 3 of 18
